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arXiv 0907.0006astro-ph.COastro-ph.GAgr-qchep-phhep-th
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暗物质的恒定表面重力和密度分布

Constant surface gravity and density profile of dark matter

H. J. de Vega, N. G. Sanchez

摘要:

累积的观测证据证实,表面重力的暗物质(DM)晕mu_{0 D} = r_0 rho_0,其中r_0和rho_0是晕核半径和中心密度,分别是几乎恒定的和独立的星系光度为大量的星系系统(螺旋,矮不规则和球状体,椭圆形)跨越14个级别的亮度和不同的哈勃类型。值得注意的是,它的数值mu_{0 D} = 140 M_{sun} /pc ^2 =(18.6 Mev)^3在所有这些系统中都大致相同(最多为2倍)。首先,我们给出了mu_{0 D}与r_0无关的物理结果:能量标度为体积sim r_0 ^3,而质量和熵标度分别为表面~ r_0 ^2和表面乘以log r_0。也就是说,熵的尺度与黑洞熵相似,但系数要小得多。其次,我们计算的表面重力和密度分布的小尺度的第一性原理和原始的密度波动的演化,因为通货膨胀的结束,直到今天使用线性化的Boltzmann-Vlasov方程。用这种方法得到的密度分布图rho_{lin}(r)在中间尺度上随r^{-1-n_s/2}而减小,其中n_s = 0.964是原始谱指数。这个标度与在观测和N体模拟中发现的经验行为非常一致:r^{-1.6 \pm 0.4}。观测到的mu_{0 D}值表明DM粒子质量m处于keV量级。理论上导出的密度分布rho_{lin}(r)在keV标度中对于m是核心的,并且它们在GeV标度或更高的标度中对于m看起来是尖点的。我们认为费米子和玻色子作为DM粒子的超相对论或非相对论去耦。我们的结果没有使用任何粒子物理模型,并与DM粒子的统计略有不同。

英文摘要:

Cumulative observational evidence confirm that the surface gravity of dark matter (DM) halo mu_{0 D} = r_0 rho_0 where r_0 and rho_0 are the halo core radius and central density, respectively, is nearly constant and independent of galaxy luminosity for a high number of galactic systems (spirals, dwarf irregular and spheroidals, elliptics) spanning over 14 magnitudes in luminosity and of different Hubble types. Remarkably, its numerical value mu_{0 D} = 140 M_{sun}/pc^2 = (18.6 Mev)^3 is approximately the same (up to a factor of two) in all these systems. First, we present the physical consequences of the independence of mu_{0 D} on r_0: the energy scales as the volume sim r_0^3 while the mass and the entropy scale as the surface ~ r_0^2 and the surface times log r_0, respectively. Namely, the entropy scales similarly to the black-hole entropy but with a much smaller coefficient. Second, we compute the surface gravity and the density profile for small scales from first principles and the evolution of primordial density fluctuations since the end of inflation till today using the linearized Boltzmann-Vlasov equation. The density profile rho_{lin}(r) obtained in this way decreases as r^{-1-n_s/2} for intermediate scales where n_s = 0.964 is the primordial spectral index. This scaling is in remarkable agreement with the empirical behaviour found observationally and in N-body simulations: r^{-1.6\pm 0.4}. The observed value of mu_{0 D} indicates that the DM particle mass m is in the keV scale. The theoretically derived density profiles rho_{lin}(r) turn to be cored for m in the keV scale and they look as cusped for m in the GeV scale or beyond. We consider both fermions and bosons as DM particles decoupling either ultrarelativistically or non-relativistically. Our results do not use any particle physics model and vary slightly with the statistics of the DM particle.

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